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Non-parametric Tests e.g., Chi-Square. Parametric Interval or ratio data Name parametric tests we covered Tuesday. Non-parametric Ordinal and nominal data. When to use various statistics. Parametric Tests. To compare two groups on Mean Scores use t-test.

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when to use various statistics
Parametric

Interval or ratio data

Name parametric tests we covered Tuesday

Non-parametric

Ordinal and nominal data

When to use various statistics
slide3

Parametric Tests

To compare two groups on Mean Scores use t-test.

For more than 2 groups use Analysis of Variance (ANOVA)

Nonparametric Tests

Can’t get a mean from nominal or ordinal data.

Chi Square tests the difference in Frequency Distributions of two or more groups.

chi square x 2
Chi-Square X2
  • Chi Square tests the difference in frequency distributions of two or more groups.
  • Test of Significance
  • of two nominal variables or
  • of a nominal variable & an ordinal variable
  • Used with a cross tabulation table
chi square

2

Chi-Square

Chi-Square =

logic of chi square analysis
Logic of Chi-Square Analysis
  • If the observed values are different enough from the expected values, you reject the null hypothesis
  • If the observed values and the expected values are similar, you fail to reject the null hypothesis
example work pregnancy
Example: Work & Pregnancy
  • The impact of working on pregnancy
  • Ha: Working during pregnancy increases the risk of miscarriage
  • H0: Working during pregnancy has NO impact on the risk of miscarriage
example work pregnancy1
Example: Work & Pregnancy
  • Suppose in general population 5 in 100 pregnancy results in miscarriage
  • Probability(p) = .05 or 5%
example work pregnancy2

Total (n=1000)

Yes

50

(5%)

No

950

(95%)

Total

1000

Example: Work & Pregnancy

Miscarriage

example work pregnancy3

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes

50 (5%)

No

950 (95%)

Total

500

500

100

Example: Work & Pregnancy
  • H0: Working during pregnancy has NO impact on the risk of miscarriage

?

Miscarriage

example work pregnancy4

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes Miscarriage

25 (5%)

25

(5%)

50 (5%)

No

475 (95%)

475 (95%)

950 (95%)

Total

500

500

100

Example:Work & Pregnancy
  • If NULL hypothesis TRUE, both work & no work groups would have same probability of miscarriage. EXPECTED values:

Miscarriage

example work pregnancy5

Work (n=500)

No Work (n=500)

Total (n=1000)

Yes Miscarriage

40 (8%)

10

(2%)

50 (5%)

No

460 (92%)

490 (98%)

950 (95%)

Total

500

500

100

Example:Work & Pregnancy
  • The actual values in your data = OBSERVED VALUES

Miscarriage

tourist expenditure mainlander vs japanese
Tourist Expenditure: Mainlander vs. Japanese

Chi-Square x2= 7.34, df = 2, p<.001

use spss crosstabs for nominal and ordinal data
Use SPSS Crosstabs (for nominal and ordinal data)
  • Click…. Analyze
  • Descriptive statistics
  • Crosstabs
  • Highlight variables for row
  • Highlight variable for column
  • Click statistics, click chi-square or correlation
  • Etc.
both chi square non parametric test and t test parametric test
Both chi square(non-parametric test) and t-test(parametric test)…
  • Examines if observed difference between groups in your data is true difference
  • True difference = difference that exists in the population
  • H0 says there is no difference in the population
which values are compared
Which values are compared?

Chi-Square

Frequencies in each cell

t-test

Mean and Standard Deviation of each group

if h 0 is true
If H0 is true…

Chi-Square

The values in the frequency table will look like Expected Values

t-test

The distribution of both groups will look like Population Distribution

chi square if h 0 is true males females no difference

Male

Female

Total

YES

30%

30%

30%

NO

70%

70%

70%

Chi- square: If H0 is true…Males = Females (No difference)
t test if h 0 is true

Total

Female

Male

t-test: If H0 is true …

# of cases

Test score

Mean

t test if h 0 is not true

Total

Female

Male

t-test: If H0 is NOT true …

# of cases

Test score

Mean

Mean

Mean

t test if h 0 is not true1

Total

Female

Male

t-test:If H0 is NOT true …

# of cases

Test score

Mean

Mean